Question

The USD/euro exchange rate is 1.3000. The exchange rate volatility is 15%. A US company willhave to pay 1 million euros in three months. The euro and USD risk-free rates are 5% and 4%,respectively. The company decides to use a range forward contract with the lower strike equal to1.2500.(a)

What should the higher strike be to create a zero-cost contract?(b)

What position in calls and puts should the company take?(c)

Show that your answer to (a) does not depend on interest rates providing the interest ratedifferential between the two currencies, r – r f , remains the same.

Answer 1

(a) A put with a strike price of 1.25 is worth $0.019. By trial and error DerivaGem can be used to show that the strike price of a call that leads to a call having a price of $0.019 is 1.3477. This is the higher strike price to create a zero cost contract.

(b) The company should sell a put with strike price 1.25 and buy a call with strike price 1.3477. This ensures that the exchange rate it pays for the euros is between 1.2500 and 1.3477.

(c) If the interest rates change so that the spread between the dollar and euro interest rates remains the same, forward prices remain the same. From equations (15.10) and (15.11). changes to r have the same proportional effect on both c and p. If the relationship c = p holds for one value of r, it holds for all values of r . as a result the answer to (a) is unchanged when the spread between the two rates is held the same.